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Leona [35]
3 years ago
7

Complete the coordinate proof of the theorem.

Mathematics
2 answers:
Flauer [41]3 years ago
8 0

Answer:


Step-by-step explanation:

THESE ARE THE CORRECT ANSWERS

mojhsa [17]3 years ago
3 0
C(a,b), because the x-coordinate( first coordinate) is a (seeing as it is situated directly above point B, which also has an x-coordinate of a) and the y-coordinate ( second coordinate) is b (seeing as it is situated on the same horizontal level as point D, which also has a y-coordinate of b)

the length of AC can be calculated with the theorem of Pythagoras:

length AB = a - 0 = a
length BC = b - 0 = b

seeing as the length of AC is the longest, it can be calculated by the following formula:

It is called "Pythagoras' Theorem" and can be written in one short equation:

a^2 + b^2 = c^2 (^ means to the power of by the way)

in this case, A and B are lengths AB and BC, so lenght AC can be calculated as the following:

a^2 + b^2 = (length AC)^2
length AC = √(a^2 + b^2)

Extra information: Seeing as the shape of the drawn lines is a rectangle, lines AC and BD have to be the same length, so BD is also √(a^2 + b^2). But that is also stated in the assignment!


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Sin^2(x/2)=sin^2x <br> Find the value of x
Veronika [31]
\sin^2\dfrac x2=\sin^2x
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1-\cos x=2-2\cos^2x
2\cos^2x-\cos x-1=0
(2\cos x+1)(\cos x-1)=0
\implies\begin{cases}2\cos x+1=0\\\cos x-1=0\end{cases}\implies\begin{cases}\cos x=-\frac12\\\cos x=1\end{cases}

The first case occurs in 0\le x for x=\dfrac{2\pi}3 and x=\dfrac{4\pi}3. Extending the domain to account for all real x, we have this happening for x=\dfrac{2\pi}3+2n\pi and \dfrac{4\pi}3+2n\pi, where n\in\mathbb Z.

The second case occurs in 0\le x when x=0, and extending to all reals we have x=2n\pi for n\in\mathbb Z, i.e. any even multiple of \pi.
6 0
3 years ago
The circumference of the earth is 2.4x109 miles. if you traveled at an average of 8.5x10 miles per hour, how long would it take
pshichka [43]

Answer:

282 hr   <======= see below

Step-by-step explanation:

Distance / rate = time

2.4 x 10^9 mi / 85 m/hr   = 28235294 hr

 You must have left the power of 10 off of your speed

     probably should be   8.5 x 10^6  perhaps?   then answer is 282

<h3>If speed was 8.5 x 10^5   then answer becomes ~ 2820   </h3>
8 0
2 years ago
Help me please fast ​
Natalija [7]

Answer:

Step-by-step explanation:

\frac{5}{x-3}+\frac{2}{x+1}=3  \\\\\frac{5(x+1)+2(x-3)}{(x-3)(x+1)} =3\\\\5x+5+2x-6=3(x-3)(x+1)\\\\7x-1=3(x^2+x-3x-3)\\\\7x-1=3(x^2-2x-3)\\\\7x-1=3x^2-6x-9\\\\0=3x^2-6x-7x-9+1\\0=3x^2-13x-8

Hence proved!

3 0
3 years ago
EXPERTS, ACES, GENIUSES, TRUSTED HELPERS, AND ELITE HELPERS ONLY PLEASE!!!
charle [14.2K]
8) factor 6+17g+10g^2
10g^2+17g+6
(5g+6)(2g+1)
C is the answer.

9) which one is a perfect square?
4x^2-14x+49 doesn't factor
4x^2-28x+49=(2x-7)(2x-7)
x^2-x+1 doesn't factor
x^2-2x+2 doesn't factor
B is the answer.

11) factor y^2-2y-48
(y+6)(y-8)
D is the answer

12) for the last one you can multiply the answers out of factor.

Sorry this took forever. It's hard to use the website cuz I'm used to the app.


Best wishes!


4 0
3 years ago
Read 2 more answers
E^4x-5-e=0 Solve the equation for x
kati45 [8]

Answer:

x =  \frac{1}{4}  \times In(5 + e)

Step-by-step explanation:

{e}^{4x}  - 5 - e = 0 \\  {e}^{4x}  = 5 + e \\ 4x = In(5 + e) \\

\boxed{Answer:{\boxed{\green{x =  \frac{1}{4}  \times In(5 + e)}}}}

8 0
3 years ago
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